CN114970121A - Generator-containing electromagnetic transient simulation iterative solution method and system - Google Patents

Generator-containing electromagnetic transient simulation iterative solution method and system Download PDF

Info

Publication number
CN114970121A
CN114970121A CN202210502080.5A CN202210502080A CN114970121A CN 114970121 A CN114970121 A CN 114970121A CN 202210502080 A CN202210502080 A CN 202210502080A CN 114970121 A CN114970121 A CN 114970121A
Authority
CN
China
Prior art keywords
generator
iterative
equation
solution
differential equation
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Pending
Application number
CN202210502080.5A
Other languages
Chinese (zh)
Inventor
高路
纪锋
林畅
林俊杰
彭逸轩
庞辉
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
State Grid Smart Grid Research Institute Co ltd
Original Assignee
State Grid Smart Grid Research Institute Co ltd
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by State Grid Smart Grid Research Institute Co ltd filed Critical State Grid Smart Grid Research Institute Co ltd
Priority to CN202210502080.5A priority Critical patent/CN114970121A/en
Publication of CN114970121A publication Critical patent/CN114970121A/en
Pending legal-status Critical Current

Links

Images

Classifications

    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00Computer-aided design [CAD]
    • G06F30/20Design optimisation, verification or simulation
    • YGENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02EREDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E60/00Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • Computer Hardware Design (AREA)
  • Evolutionary Computation (AREA)
  • Geometry (AREA)
  • General Engineering & Computer Science (AREA)
  • General Physics & Mathematics (AREA)
  • Management, Administration, Business Operations System, And Electronic Commerce (AREA)

Abstract

An electromagnetic transient simulation iterative solution method and system containing a generator comprises the following steps: establishing a unified nonlinear differential equation for the generator and the circuit system based on electromagnetic transient simulation of the generator; dispersing the unified nonlinear differential equation by adopting an integration method to obtain a dispersed equation; carrying out iterative solution on the dispersed equation by using a Newton iterative method to obtain a solution in each time step; according to the invention, through the integral differential equation of the column writing power system, the nonlinear equation is solved by using the Newton Raphson method, so that iterative solution of the motor and the circuit system in a time step can be realized, and the numerical divergence problem caused by separate solution delay of the motor and the circuit system or the numerical stability and precision problem caused by inaccurate prediction method are solved.

Description

Generator-containing electromagnetic transient simulation iterative solution method and system
Technical Field
The invention relates to the field of electromagnetic transient simulation of a power system, in particular to an electromagnetic transient simulation iterative solution method and system with a generator.
Background
In the existing electromagnetic transient simulation, a nonlinear element such as a generator is generally equivalent to a controlled source and a main circuit for connection calculation, and the value of the controlled source is generally updated by two ways. 1. Some unknown quantities at the t moment need to be predicted from the solution at the known t-delta t moment, the result accuracy depends on the adopted prediction method, and the numerical value is unstable due to improper selection of the prediction method; 2. by adopting the known quantity calculation at the time of t-delta t, the numerical divergence problem caused by time delay can exist, and the time delay needs to be compensated and corrected. Both of the above two methods have a problem of numerical stability, and the numerical stability can be further improved only by changing the solution method from direct solution to iterative solution in each time step.
Disclosure of Invention
In order to solve the problem of numerical stability of generator electromagnetic transient simulation in the prior art, the invention provides an electromagnetic transient simulation iterative solution method containing a generator, which comprises the following steps:
establishing a unified nonlinear differential equation for the generator and the circuit system based on electromagnetic transient simulation of the generator;
dispersing the unified nonlinear differential equation by adopting an integration method to obtain a dispersed equation;
and carrying out iterative solution on the dispersed equation by using a Newton iterative method to obtain a solution in each time step.
Preferably, the discretizing the unified nonlinear differential equation by an integration method to obtain a discretized equation includes:
converting the unified nonlinear differential equation into a first-order nonlinear differential equation;
and dispersing the first-order nonlinear differential equation by using different integration methods to obtain a dispersed equation.
Preferably, the discretizing the first-order nonlinear differential equation by using different integration methods to obtain a discretized equation includes:
adding a formula obtained by multiplying the first-order nonlinear differential equation by 1-beta at the time t and a formula obtained by multiplying the first-order nonlinear differential equation by beta at the time t + delta t to obtain a calculation formula for calculating the time t + delta t from the time t;
multiplying the equation obtained by multiplying the differential equation of the order of non-linearity by 1-beta at time t by
Figure BDA0003634755160000021
And then, subtracting the calculation formula for calculating the t + delta t moment from the t moment to obtain the equation after dispersion.
Preferably, the unified non-linear differential equation is calculated as follows:
Figure BDA0003634755160000022
in the formula, n is the number of circuit nodes, nm is the number of mass blocks of a mechanical shafting of the motor, L (theta) is a generator inductance matrix, B is a generator winding and node correlation matrix, J is a generator shafting rotation inertia matrix, D is a damping matrix, K is an elastic coefficient matrix, T is a generator mechanical torque vector, and K is a generator mechanical torque vector C Is a capacitance coefficient matrix, K R Is a matrix of resistivity, K L The inductance coefficient matrix is shown, psi is a node flux linkage, and theta is a rotation angle of a motor shafting.
Preferably, the iteratively solving the discretized equation by using a newton iteration method to obtain a solution in each time step includes:
converting the discretized equation into a functional expression and acquiring a Jacobian matrix of the functional expression;
converting the Jacobian matrix into an iterative expression which can utilize a Newton iterative method;
and carrying out iterative solution on the iterative formula by using a Newton iterative method to obtain a solution in each time step.
Preferably, the iterative solution of the iterative equation by using a newton iteration method to obtain a solution in each time step includes:
will | < f (x) N+1,k+1 ) II is and is providedComparing the determined error values, if the error values are smaller than the set error values, finishing the calculation, otherwise, solving according to an iterative expression of a Newton iterative method, and x N+1,k+1 Is an estimated value of the (k + 1) th iteration, k is the iteration number, x is the state quantity, f (x) N+1,k+1 ) And calculating a function value of the (k + 1) th iteration calculated in the (N + 1) th step, wherein N is the calculated in the Nth step.
Preferably, the iteration formula using the newton iteration method is as follows:
Figure BDA0003634755160000023
in the formula, x N+1,k Is an initial estimate at time t + Δ t, x N+1,k+1 Is the new result estimate, i.e., the initial estimate of the next iteration.
Based on the same inventive concept, the invention also provides an electromagnetic transient simulation iterative solution system with a generator, which comprises:
the differential equation establishing module is used for establishing a unified nonlinear differential equation for the generator and the circuit system based on the electromagnetic transient simulation of the generator;
the differential equation dispersing module is used for dispersing the unified nonlinear differential equation by adopting an integral method to obtain a dispersed equation;
and the iterative solution module is used for carrying out iterative solution on the dispersed equation by utilizing a Newton iterative method to obtain a solution in each time step.
Preferably, the discrete module of differential equations includes:
the conversion submodule is used for converting the unified nonlinear differential equation into a first-order nonlinear differential equation;
and the discrete submodule is used for dispersing the first-order nonlinear differential equation by using different integration methods to obtain a dispersed equation.
Preferably, the discrete sub-modules are specifically configured to:
adding a formula obtained by multiplying the first-order nonlinear differential equation by 1-beta at the time t and a formula obtained by multiplying the first-order nonlinear differential equation by beta at the time t + delta t to obtain a calculation formula for calculating the time t + delta t from the time t;
multiplying the formula obtained by multiplying the first-order nonlinear differential equation at the time t by 1-beta by
Figure BDA0003634755160000031
And then, subtracting the calculation formula for calculating the t + delta t moment from the t moment to obtain the equation after dispersion.
Preferably, the unified non-linear differential equation is calculated as follows:
Figure BDA0003634755160000032
in the formula, n is the number of circuit nodes, nm is the number of mass blocks of a mechanical shafting of the motor, L (theta) is a generator inductance matrix, B is a generator winding and node correlation matrix, J is a generator shafting rotation inertia matrix, D is a damping matrix, K is an elastic coefficient matrix, T is a generator mechanical torque vector, and K is a generator mechanical torque vector C Is a capacitance coefficient matrix, K R Is a matrix of resistivity, K L The inductance coefficient matrix is shown, psi is a node flux linkage, and theta is a rotation angle of a motor shafting.
Preferably, the iterative solution module includes:
the functional formula submodule is used for converting the dispersed equation into a functional formula and acquiring a Jacobian matrix of the functional formula;
the iterative expression submodule is used for converting the Jacobian matrix into an iterative expression which can utilize a Newton iterative method;
and the solving submodule is used for carrying out iterative solution on the iterative expression by utilizing a Newton iterative method to obtain a solution in each time step.
Preferably, the solving submodule is specifically configured to:
will | < f (x) N+1,k+1 ) II, comparing with a set error value, finishing the calculation if the difference is less than the set error value, otherwise solving according to an iterative formula of a Newton iterative method, and x N+1,k+1 Is an estimated value of the (k + 1) th iteration, k is the iteration number, x is the state quantity, f (x) N+1,k+1 ) And calculating a function value of the (k + 1) th iteration calculated in the (N + 1) th step, wherein N is the calculated in the Nth step.
Preferably, the iteration formula using the newton iteration method is as follows:
Figure BDA0003634755160000041
in the formula, x N+1k Is an initial estimate of time t + Δ t, x N+1,k+1 Is the new result estimate, i.e., the initial estimate of the next iteration.
Compared with the prior art, the invention has the beneficial effects that:
an electromagnetic transient simulation iterative solution method and system containing a generator comprises the following steps: establishing a unified nonlinear differential equation for the generator and the circuit system based on electromagnetic transient simulation of the generator; dispersing the unified nonlinear differential equation by adopting an integration method to obtain a dispersed equation; carrying out iterative solution on the dispersed equation by using a Newton iterative method to obtain a solution in each time step; according to the invention, through the integral differential equation of the column writing power system, the nonlinear equation is solved by using the Newton Raphson method, so that iterative solution of the motor and the circuit system in a time step can be realized, and the numerical divergence problem caused by separate solution delay of the motor and the circuit system or the numerical stability and precision problem caused by inaccurate prediction method are solved.
Drawings
FIG. 1 is a flow chart of an electromagnetic transient simulation iterative solution method for a generator according to the present invention;
FIG. 2 is a flow chart of each time step iteration solution of the present invention.
Detailed Description
The invention provides an iterative solution method for generator-containing electromagnetic transient simulation, which aims at the problem of numerical stability existing when the electromagnetic transient simulation of a generator is equivalent to the connection of a controlled source and a circuit, establishes a unified differential equation between the generator and a circuit system, and carries out iterative solution on the integral equation by using a Newton-Raphson iteration method, thereby fundamentally avoiding the problem of numerical stability caused by the time delay or a prediction method when the generator is equivalent to the controlled source.
Example 1:
an electromagnetic transient simulation iterative solution method for a generator, the specific process of which is shown in fig. 1, comprises:
step 1, establishing a unified nonlinear differential equation for a generator and a circuit system based on electromagnetic transient simulation of the generator;
step 2, dispersing the unified nonlinear differential equation by adopting an integral method to obtain a dispersed equation;
and 3, carrying out iterative solution on the dispersed equation by using a Newton iteration method to obtain a solution in each time step.
The following describes an iterative solution method for generator-containing electromagnetic transient simulation according to the present invention in detail with reference to fig. 2.
In step 1, establishing a unified nonlinear differential equation for the generator and the circuit system based on electromagnetic transient simulation of the generator, specifically comprising:
differential equations in the time domain solution for column written power systems:
Figure BDA0003634755160000051
in the formula, K C Is a capacitance coefficient matrix, K R Is a matrix of resistivity, K L For the inductance matrix, Ψ is the node flux linkage.
The extended column writes the differential equation containing the generator:
Figure BDA0003634755160000052
wherein n is the number of circuit nodes, and nm is the number of mass blocks of the mechanical shafting of the motor. L (theta) is a generator inductance matrix and is changed along with the rotation angle of the generator, and B is a generator winding and node correlation matrix. J is a generator shafting rotational inertia matrix, D is a damping matrix, K is an elastic coefficient matrix, and T is a generator mechanical torque vector.
In step 2, dispersing the unified nonlinear differential equation by an integration method to obtain a dispersed equation, which specifically includes:
the electromagnetic transient simulation of the power system is to solve a differential equation shown in formula (2).
The equation (2) is a second order differential equation, and needs to be transformed into a first order differential equation for computer solution. Transforming equation (2) into:
Figure BDA0003634755160000061
wherein,
Figure BDA0003634755160000062
Figure BDA0003634755160000063
e is an identity matrix, and E is an identity matrix,
Figure BDA0003634755160000064
Figure BDA0003634755160000065
discretizing equation (3) using different integration methods:
Figure BDA0003634755160000066
where Δ t is the discrete time step, x N Is the state quantity at time t, x N+1 Beta is a selection factor of different integration methods for the state quantity at the moment t + delta t. When beta is 0.5, the trapezoidal integration method is adopted; when β is 1, it is the receding euler method.
At time t, multiplying equation (3) by 1- β to obtain:
Figure BDA0003634755160000067
at time t + Δ t, β is multiplied by equation (3) to obtain:
Figure BDA0003634755160000068
calculating time t + delta t from time t, K 1 And K 2 Keeping the same, equation (5) and equation (6) are added to obtain:
Figure BDA0003634755160000069
multiplying equation (5) by
Figure BDA00036347551600000610
Obtaining:
Figure BDA0003634755160000071
equation (7) is subtracted from equation (8):
Figure BDA0003634755160000072
further simplified formula (9) is obtained:
Ax N+1 =Bx N +(1-β)R(x N )+βR(x N+1 ) (10)
wherein,
Figure BDA0003634755160000073
due to R (x) in the formula (10) N ) And R (x) N+1 ) Is about x N And x N+1 So equation (10) is a non-linear equation.
In step 3, using a newton iteration method to iteratively solve the discretized equation to obtain a solution in each time step, specifically including:
the unknown variable in formula (10) is x N+1 And x is N And R (x) N ) Are all known amounts. In order to solve using the newton iteration method, equation (10) needs to be changed into the form of equation (11), i.e. to solve f (x) N+1 )=0。
f(x N+1 )=-Ax N+1 +Bx N +(1-β)R(x N )+βR(x N+1 )=0 (11)
Function f (x) N+1 ) The Jacobian matrix of:
Figure BDA0003634755160000074
wherein,
Figure BDA0003634755160000075
Γ(θ)= (L(θ)) -1
Figure BDA0003634755160000076
and
Figure BDA0003634755160000077
are all matrix functions related to theta and can be specifically determined according to the type and parameters of the motor.
The iteration formula using the newton iteration method is:
Figure BDA0003634755160000078
wherein x N+1,k Is an initial estimate at time t + Δ t, x N+1,k+1 Is the new result estimate, i.e., the initial estimate of the next iteration. When | f (x) N+1,k+1 ) When |, is less than the set allowable error, the iterative solution in each time step is completed.
Example 2:
an electromagnetic transient simulation iterative solution system with a generator, comprising:
the differential equation establishing module is used for establishing a unified nonlinear differential equation for the generator and the circuit system based on the electromagnetic transient simulation of the generator;
the differential equation dispersing module is used for dispersing the unified nonlinear differential equation by adopting an integral method to obtain a dispersed equation;
and the iterative solution module is used for carrying out iterative solution on the dispersed equation by utilizing a Newton iterative method to obtain a solution in each time step.
The discrete module of differential equations comprises:
the conversion submodule is used for converting the unified nonlinear differential equation into a first-order nonlinear differential equation;
and the discrete submodule is used for dispersing the first-order nonlinear differential equation by using different integration methods to obtain a discrete equation.
The iterative solution module comprises:
the functional formula submodule is used for converting the dispersed equation into a functional formula and acquiring a Jacobian matrix of the functional formula;
the iterative expression submodule is used for converting the Jacobian matrix into an iterative expression which can utilize a Newton iterative method;
and the solving submodule is used for carrying out iterative solution on the iterative expression by utilizing a Newton iterative method to obtain a solution in each time step.
A differential equation establishing module, specifically configured to:
differential equations in the time domain solution for column written power systems:
Figure BDA0003634755160000081
in the formula, K C Is a capacitance coefficient matrix, K R Is a matrix of resistivity, K L Psi is the node flux linkage.
The extended column writes the differential equation containing the generator:
Figure BDA0003634755160000082
wherein n is the number of circuit nodes, and nm is the number of mass blocks of the mechanical shafting of the motor. L (theta) is a generator inductance matrix which is changed along with the rotation angle of the generator, and B is a correlation matrix of the generator winding and the node. J is a generator shafting rotational inertia matrix, D is a damping matrix, K is an elastic coefficient matrix, and T is a generator mechanical torque vector.
A conversion submodule, specifically configured to:
the electromagnetic transient simulation of the power system is to solve a differential equation shown in formula (2).
The equation (2) is a second order differential equation, and needs to be transformed into a first order differential equation for computer solution. Transforming equation (2) into:
Figure BDA0003634755160000091
wherein,
Figure BDA0003634755160000092
Figure BDA0003634755160000093
e is a unit matrix, and E is a unit matrix,
Figure BDA0003634755160000094
Figure BDA0003634755160000095
discrete sub-modules, specifically configured to:
discretizing equation (3) using different integration methods:
Figure BDA0003634755160000096
where Δ t is the discrete time step, x N Is the state quantity at time t, x N+1 Beta is a selection factor of different integration methods for the state quantity at the moment t + delta tAnd (4) adding the active ingredients. When beta is 0.5, the method is a trapezoidal integration method; when β is 1, it is determined by the retropulsion euler method.
At time t, multiplying equation (3) by 1- β to obtain:
Figure BDA0003634755160000097
at time t + Δ t, β is multiplied by equation (3) to obtain:
Figure BDA0003634755160000101
calculating t + delta t time from t time, K 1 And K 2 Keeping the same, equation (5) and equation (6) are added to obtain:
Figure BDA0003634755160000102
multiplying equation (5) by
Figure BDA0003634755160000103
Obtaining:
Figure BDA0003634755160000104
equation (7) is subtracted from equation (8):
Figure BDA0003634755160000105
further simplified formula (9) is obtained:
Ax N+1 =Bx N +(1-β)R(x N )+βR(x N+1 ) (10)
wherein,
Figure BDA0003634755160000106
due to R (x) in the formula (10) N ) And R (x) N+1 ) Is about x N And x N+1 So equation (10) is a non-linear equation.
A functional submodule, specifically configured to:
the unknown variable in formula (10) is x N+1 And x is N And R (x) N ) Are all known quantities. In order to solve using the newton iteration method, equation (10) needs to be changed into the form of equation (11), i.e. to solve f (x) N+1 )=0。
f(x N+1 )=-Ax N+1 +Bx N +(1-β)R(x N )+βR(x N+1 )=0 (11)
Function f (x) N+1 ) The Jacobian matrix of:
Figure BDA0003634755160000107
wherein,
Figure BDA0003634755160000108
Γ(θ)= (L(θ)) -1
Figure BDA0003634755160000109
and
Figure BDA00036347551600001010
are all matrix functions related to theta and can be specifically determined according to the type and parameters of the motor.
The iterative sub-module is specifically configured to:
the iteration formula using the newton iteration method is:
Figure BDA0003634755160000111
wherein x N+1,k Is the initial estimate at time t + Δ t, x N+1,k+1 Is the new result estimate, i.e., the initial estimate of the next iteration.
A solving submodule, specifically configured to:
when | f (x) N+1,k+1 ) When |, is less than the set allowable error, the iterative solution in each time step is completed.
As will be appreciated by one skilled in the art, embodiments of the present invention may be provided as a method, system, or computer program product. Accordingly, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The present invention is not limited to the above embodiments, and any modifications, equivalent substitutions, improvements, etc. within the spirit and principle of the present invention are included in the scope of the claims of the present invention.

Claims (14)

1. An electromagnetic transient simulation iterative solution method for a generator, comprising:
establishing a unified nonlinear differential equation for the generator and the circuit system based on electromagnetic transient simulation of the generator;
dispersing the unified nonlinear differential equation by adopting an integration method to obtain a dispersed equation;
and carrying out iterative solution on the dispersed equation by using a Newton iterative method to obtain a solution in each time step.
2. The iterative solution method for generator-included electromagnetic transient simulation according to claim 1, wherein the discretizing the unified nonlinear differential equation by an integration method to obtain a discretized equation comprises:
converting the unified nonlinear differential equation into a first-order nonlinear differential equation;
and dispersing the first-order nonlinear differential equation by using different integration methods to obtain a dispersed equation.
3. The iterative generator-based electromagnetic transient simulation solution method of claim 2, wherein discretizing the first-order nonlinear differential equation by different integration methods to obtain a discretized equation comprises:
adding a formula obtained by multiplying the first-order nonlinear differential equation by 1-beta at the time t and a formula obtained by multiplying the first-order nonlinear differential equation by beta at the time t + delta t to obtain a calculation formula for calculating the time t + delta t from the time t;
multiplying the formula obtained by multiplying the first-order nonlinear differential equation at the time t by 1-beta by
Figure FDA0003634755150000011
And then, subtracting the calculation formula for calculating the t + delta t moment from the t moment to obtain the equation after dispersion.
4. The iterative generator-based electromagnetic transient simulation solution method of claim 1, wherein the unified nonlinear differential equation is calculated as follows:
Figure FDA0003634755150000012
in the formula, n is the number of circuit nodes, nm is the number of mass blocks of a mechanical shafting of the motor, L (theta) is a generator inductance matrix, B is an incidence matrix of a generator winding and the nodes, J is a generator shafting rotation inertia matrix, D is a damping matrix, K is an elastic coefficient matrix, T is a generator mechanical torque vector, and K is a generator mechanical torque vector C Is a capacitance coefficient matrix, K R Is a matrix of resistivity, K L The inductance coefficient matrix is shown, psi is a node flux linkage, and theta is a rotation angle of a motor shafting.
5. The iterative solution method for generator-included electromagnetic transient simulation according to claim 1, wherein the iterative solution of the discretized equation by using a newton iteration method to obtain a solution in each time step comprises:
converting the discretized equation into a functional expression and acquiring a Jacobian matrix of the functional expression;
converting the Jacobian matrix into an iterative expression which can utilize a Newton iterative method;
and carrying out iterative solution on the iterative formula by using a Newton iterative method to obtain a solution in each time step.
6. The iterative solution method for generator-included electromagnetic transient simulation according to claim 5, wherein the iterative solution of the iterative equation by using the newton iteration method to obtain a solution in each time step comprises:
will | < f (x) N+1,k+1 ) II, comparing with a set error value, finishing the calculation if the difference is less than the set error value, otherwise solving according to an iterative formula of a Newton iterative method, and x N+1,k+1 Is an estimated value of the (k + 1) th iteration, k is the iteration number, x is the state quantity, f (x) N+1,k+1 ) And calculating a function value of the (k + 1) th iteration calculated in the (N + 1) th step, wherein N is the calculated in the Nth step.
7. The method of claim 5, wherein the iteration formula using the Newton's iteration method is as follows:
Figure FDA0003634755150000021
in the formula, x N+1,k Is an initial estimate of time t + Δ t, x N+1,k+1 Is the new result estimate, i.e., the initial estimate of the next iteration.
8. An electromagnetic transient simulation iterative solution system with a generator, comprising:
the differential equation establishing module is used for establishing a unified nonlinear differential equation for the generator and the circuit system based on the electromagnetic transient simulation of the generator;
the differential equation dispersing module is used for dispersing the unified nonlinear differential equation by adopting an integral method to obtain a dispersed equation;
and the iterative solution module is used for carrying out iterative solution on the dispersed equation by utilizing a Newton iterative method to obtain a solution in each time step.
9. The iterative generator-based electromagnetic transient simulation solution system of claim 8, wherein the discrete differential equation module comprises:
the conversion submodule is used for converting the unified nonlinear differential equation into a first-order nonlinear differential equation;
and the discrete submodule is used for dispersing the first-order nonlinear differential equation by using different integration methods to obtain a discrete equation.
10. The electromagnetic transient simulation iterative solution system with a generator of claim 9, wherein the discrete sub-modules are specifically configured to:
adding a formula obtained by multiplying the first-order nonlinear differential equation by 1-beta at the time t and a formula obtained by multiplying the first-order nonlinear differential equation by beta at the time t + delta t to obtain a calculation formula for calculating the time t + delta t from the time t;
multiplying the formula obtained by multiplying the first-order nonlinear differential equation at the time t by 1-beta by
Figure FDA0003634755150000031
And then, subtracting the calculation formula for calculating the t + delta t moment from the t moment to obtain the equation after dispersion.
11. The iterative generator-based electromagnetic transient simulation solution system of claim 8, wherein the unified differential equation is calculated as follows:
Figure FDA0003634755150000032
in the formula, n is the number of circuit nodes, nm is the number of mass blocks of a mechanical shafting of the motor, L (theta) is a generator inductance matrix, B is a generator winding and node correlation matrix, J is a generator shafting rotation inertia matrix, D is a damping matrix, K is an elastic coefficient matrix, T is a generator mechanical torque vector, and K is a generator mechanical torque vector C Is a capacitance coefficient matrix, K R Is a matrix of resistivity, K L Is a matrix of inductance coefficients, and is,psi is the node flux linkage, theta is the motor shaft system rotation angle.
12. The generator-containing electromagnetic transient simulation iterative solution system of claim 8, wherein the iterative solution module comprises:
the functional formula submodule is used for converting the dispersed equation into a functional formula and acquiring a Jacobian matrix of the functional formula;
the iterative expression submodule is used for converting the Jacobian matrix into an iterative expression which can utilize a Newton iterative method;
and the solving submodule is used for carrying out iterative solution on the iterative expression by utilizing a Newton iterative method to obtain a solution in each time step.
13. The iterative generator-based electromagnetic transient simulation solving system of claim 12, wherein the solving submodule is specifically configured to:
will | < f (x) N+1,k+1 ) II, comparing with a set error value, finishing the calculation if the error value is smaller than the set error value, otherwise solving according to an iteration formula of a Newton iteration method, and x N+1,k+1 Is an estimated value of the (k + 1) th iteration, k is the iteration number, x is the state quantity, f (x) N+1,k+1 ) And calculating a function value of the (k + 1) th iteration calculated in the (N + 1) th step, wherein N is the calculated in the Nth step.
14. The iterative generator-based electromagnetic transient simulation solution system of claim 12, wherein the iteration formula using the newton's iteration method is as follows:
Figure FDA0003634755150000041
in the formula, x N+1,k Is an initial estimate of time t + Δ t, x N+1,k+1 Is the new result estimate, i.e., the initial estimate of the next iteration.
CN202210502080.5A 2022-05-09 2022-05-09 Generator-containing electromagnetic transient simulation iterative solution method and system Pending CN114970121A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202210502080.5A CN114970121A (en) 2022-05-09 2022-05-09 Generator-containing electromagnetic transient simulation iterative solution method and system

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202210502080.5A CN114970121A (en) 2022-05-09 2022-05-09 Generator-containing electromagnetic transient simulation iterative solution method and system

Publications (1)

Publication Number Publication Date
CN114970121A true CN114970121A (en) 2022-08-30

Family

ID=82982282

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202210502080.5A Pending CN114970121A (en) 2022-05-09 2022-05-09 Generator-containing electromagnetic transient simulation iterative solution method and system

Country Status (1)

Country Link
CN (1) CN114970121A (en)

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116720338A (en) * 2023-05-30 2023-09-08 杭州盛星能源技术有限公司 Electromagnetic transient parallel iteration real-time simulation compensation method and device

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116720338A (en) * 2023-05-30 2023-09-08 杭州盛星能源技术有限公司 Electromagnetic transient parallel iteration real-time simulation compensation method and device
CN116720338B (en) * 2023-05-30 2024-02-02 杭州盛星能源技术有限公司 Electromagnetic transient parallel iteration real-time simulation compensation method and device

Similar Documents

Publication Publication Date Title
Bauchau et al. Review of contemporary approaches for constraint enforcement in multibody systems
CN101950315B (en) Methods and apparatus to compensate first principle-based simulation models
Medvedev et al. Fitted modifications of Runge‐Kutta pairs of orders 6 (5)
Palmieri A global existence result for a semilinear scale‐invariant wave equation in even dimension
Medvedev et al. Hybrid, phase–fitted, four–step methods of seventh order for solving x ″(t)= f (t, x)
Hu et al. Pole-residue method for numerical dynamic analysis
Lehotzky et al. A pseudospectral tau approximation for time delay systems and its comparison with other weighted‐residual‐type methods
Lloret‐Cabot et al. Error behaviour in explicit integration algorithms with automatic substepping
Houska et al. Towards rigorous robust optimal control via generalized high‐order moment expansion
CN114970121A (en) Generator-containing electromagnetic transient simulation iterative solution method and system
Großeholz et al. A stabilized central difference scheme for dynamic analysis
Duarte Laudon et al. Stability of the time‐domain analysis method including a frequency‐dependent soil–foundation system
Chen et al. Explicit parallel co-simulation approach: analysis and improved coupling method based on H-infinity synthesis
Benedikt et al. Relaxing stiff system integration by smoothing techniques for non-iterative co-simulation
Jin et al. Global practical tracking for nonlinear systems with more unknowns via adaptive output‐feedback
Gonçalves et al. Moving frames and conservation laws for Euclidean invariant Lagrangians
Pindza et al. Robust spectral method for numerical valuation of european options under Merton's jump‐diffusion model
Chen et al. Stability analysis of direct integration algorithms applied to MDOF nonlinear structural dynamics
Khusnutdinova et al. D'Alembert‐type solution of the Cauchy problem for the Boussinesq‐Klein‐Gordon equation
Fang et al. Finite‐time stabilization for a class of stochastic output‐constrained systems by output feedback
Abidi A robust discrete‐time adaptive control approach for systems with almost periodic time‐varying parameters
Singh et al. A novel two‐parameter class of optimized hybrid block methods for integrating differential systems numerically
CN106611078A (en) Efficient explicit finite element analysis of a product with a time step size control scheme
Huang et al. Robust control for one‐sided Lipschitz non‐linear systems with time‐varying delays and uncertainties
Kumar et al. A novel accurate and computationally efficient integration approach to viscoplastic constitutive model

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication